This paper proposes a bidirectional rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. The proposed algorithm, called HyRRT-Connect, propagates in both forward and backward directions in hybrid time until an overlap between the forward and backward propagation results is detected. Then, HyRRT-Connect constructs a motion plan through the reversal and concatenation of functions defined on hybrid time domains, ensuring that the motion plan satisfies the given hybrid dynamics. To address the potential discontinuity along the flow caused by tolerating some distance between the forward and backward partial motion plans, we reconstruct the backward partial motion plan by a forward-in-hybrid-time simulation from the final state of the forward partial motion plan. effectively eliminating the discontinuity. The proposed algorithm is applied to an actuated bouncing ball system and a walking robot example to highlight its computational improvement.

本研究解决了混合系统的运动规划问题，填补了现有算法在双向探索方面的空白。提出的HyRRT-Connect算法通过在混合时间中双向传播，确保构建的运动计划符合混合动态，显著减少了规划过程中的不连续性。实验表明，该算法在执行能力上优于传统方法，展示了其在复杂动态系统中的潜在应用价值。

HyRRT-Connect：混合动态系统的双向运动规划